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Recent questions and answers in Numerical Methods

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1

GATE CSE 1987 | Question: 1-xxiv
The simplex method is so named because It is simple. It is based on the theory of algebraic complexes. The simple pendulum works on this method. No one thought of a better name.

Arjun answered in Numerical Methods May 26, 2022

by Arjun

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2

NIELIT 2016 MAR Scientist B - Section B: 7
In which of the following methods proper choice of initial value is very important? Bisection method False position Newton-Raphson Bairsto method

33 answered in Numerical Methods Mar 16, 2022

by 33

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8 votes

3 answers

3

GATE IT 2006 | Question: 28
The following definite integral evaluates to $\int_{-\infty}^{0} e^ {-\left(\frac{x^2}{20} \right )}dx$ $\frac{1}{2}$ $\pi \sqrt{10}$ $\sqrt{10}$ $\pi$

ankitgupta.1729 answered in Numerical Methods Sep 14, 2021

by ankitgupta.1729

3.6k views

1 vote

3 answers

4

GATE CSE 2008 | Question: 21
The minimum number of equal length subintervals needed to approximate $\int_1^2 xe^x\,dx$ to an accuracy of at least $\frac{1}{3}\times10^{-6}$ using the trapezoidal rule is 1000e 1000 100e 100

omji-mishra answered in Numerical Methods Aug 3, 2021

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2 votes

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5

GATE CSE 1988 | Question: 1i
Loosely speaking, we can say that a numerical method is unstable if errors introduced into the computation grow at _________ rate as the computation proceeds.

Jhaiyam answered in Numerical Methods Aug 1, 2020

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2 votes

2 answers

6

UGC NET CSE | June 2019 | Part 2 | Question: 10
Consider an LPP given as $\text{Max } Z=2x_1-x_2+2x_3$ subject to the constraints $2x_1+x_2 \leq 10 \\ x_1+2x_2-2x_3 \leq 20 \\ x_1 + 2x_3 \leq 5 \\ x_1, \: x_2 \: x_3 \geq 0 $ What shall be the solution of the LLP after applying first iteration of the Simplex Method ... $x_1 = 0, x_2=0, \: x_3=10, \: Z=20$

Tiklu_95 answered in Numerical Methods Jun 9, 2020

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7

UGC NET CSE | December 2018 | Part 2 | Question: 8
In PERT/CPM, the merge event represents _____ of two or more events. completion beginning splitting joining

Nbhardwaj answered in Numerical Methods May 14, 2020

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8

NIELIT 2017 OCT Scientific Assistant A (CS) - Section C: 7
The convergence of the bisection method is Cubic Quadratic Linear None

DIBAKAR MAJEE answered in Numerical Methods Apr 24, 2020

by DIBAKAR MAJEE

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9

NIELIT 2016 MAR Scientist C - Section B: 1
Choose the most appropriate option. The Newton-Raphson iteration $x_{n+1}=\dfrac{x_{n}}{2}+\dfrac{3}{2x_{n}}$ can be used to solve the equation $x^{2}=3$ $x^{3}=3$ $x^{2}=2$ $x^{3}=2$

Lakshman Bhaiya asked in Numerical Methods Apr 2, 2020

by Lakshman Bhaiya

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10

NIELIT 2017 OCT Scientific Assistant A (IT) - Section B: 17
The convergence of the bisection method is Cubic Quadratic Linear None closed

Lakshman Bhaiya asked in Numerical Methods Apr 1, 2020

by Lakshman Bhaiya

192 views

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2 answers

11

NIELIT 2017 DEC Scientist B - Section B: 3
Using bisection method, one root of $x^4-x-1$ lies between $1$ and $2$. After second iteration the root may lie in interval: $(1.25,1.5)$ $(1,1.25)$ $(1,1.5)$ None of the options.

Lakshman Bhaiya asked in Numerical Methods Mar 30, 2020

by Lakshman Bhaiya

1.9k views

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1 answer

12

NIELIT 2017 DEC Scientist B - Section B: 20
Let $u$ and $v$ be two vectors in $R^2$ whose Eucledian norms satisfy $\mid u\mid=2\mid v \mid$. What is the value $\alpha$ such that $w=u+\alpha v$ bisects the angle between $u$ and $v$? $2$ $1$ $\dfrac{1}{2}$ $-2$

Lakshman Bhaiya asked in Numerical Methods Mar 30, 2020

by Lakshman Bhaiya

376 views

2 votes

1 answer

13

Is reading comprehension asked in IIITH
Does in iiith pgeee exam , does Reading comprehension is being asked. Do we need to prepare for it?

Winner answered in Numerical Methods Mar 29, 2019

by Winner

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4 votes

2 answers

14

ISRO2009-48
The cubic polynomial $y(x)$ which takes the following values: $y(0)=1, y(1)=0, y(2)=1$ and $y(3)=10$ is $x^3 +2x^2 +1$ $x^3 +3x^2 -1$ $x^3 +1$ $x^3 -2x^2 +1$

Devwritt answered in Numerical Methods Mar 10, 2019

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3 answers

15

GATE CSE 1994 | Question: 3.4
Match the following items (i) Newton-Raphson (a) Integration (ii) Runge-Kutta (b) Root finding (iii) Gauss-Seidel (c) Ordinary Differential Equations (iv) Simpson's Rule (d) Solution of Systems of Linear Equations

Gurdeep Saini answered in Numerical Methods Dec 17, 2018

by Gurdeep Saini

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8 votes

1 answer

16

ISRO2009-44
A root $\alpha$ of equation $f(x)=0$ can be computed to any degree of accuracy if a 'good' initial approximation $x_0$ is chosen for which $f(x_0) > 0$ $f (x_0) f''(x_0) > 0$ $f(x_0) f'' (x_0) < 0$ $f''(x_0) >0$

Roman224 answered in Numerical Methods Oct 7, 2018

2.6k views

1 vote

2 answers

17

Number Theory
A prison houses 100 inmates, one in each of 100 cells, guarded by a total of 100 warders. One evening, all the cells are locked and the keys left in the locks. As the first warder leaves, she turns every key, unlocking all the doors. The second warder ... every third key and so on. Finally the last warder turns the key in just the last cell. Which doors are left unlocked and why?

Subarna Das answered in Numerical Methods Apr 19, 2018

519 views

8 votes

3 answers

18

ISRO2017-3
Using Newton-Raphson method, a root correct to 3 decimal places of $x^3 - 3x -5 = 0$ 2.222 2.275 2.279 None of the above

stanchion answered in Numerical Methods Feb 27, 2018

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19

GATE CSE 1987 | Question: 11b
Use Simpson's rule with $h=0.25$ to evaluate $ V= \int_{0}^{1} \frac{1}{1+x} dx$ correct to three decimal places. closed

makhdoom ghaya asked in Numerical Methods Nov 15, 2016

by makhdoom ghaya

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20

GATE CSE 1987 | Question: 11a
Given $f(300)=2,4771; f(304) = 2.4829; f(305) = 2.4843$ and $f(307) = 2.4871$ find $f(301)$ using Lagrange's interpolation formula. closed

makhdoom ghaya asked in Numerical Methods Nov 15, 2016

by makhdoom ghaya

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21

GATE CSE 1987 | Question: 1-xxv
Which of the following statements is true in respect of the convergence of the Newton-Rephson procedure? It converges always under all circumstances. It does not converge to a tool where the second differential coefficient changes sign. It does not converge to a root where the second differential coefficient vanishes. None of the above. closed

makhdoom ghaya asked in Numerical Methods Nov 9, 2016

by makhdoom ghaya

568 views

3 votes

1 answer

22

UGC NET CSE | December 2014 | Part 3 | Question: 69
Five men are available to do five different jobs. From past records, the time (in hours) that each man takes to do each job is known and is given in the following table : Find out the minimum time required to complete all the jobs. $5$ $11$ $13$ $15$

Sanjay Sharma answered in Numerical Methods Aug 2, 2016

by Sanjay Sharma

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3 votes

2 answers

23

ISRO-2013-48
The Guass-Seidal iterative method can be used to solve which of the following sets? Linear algebraic equations Linear and non-linear algebraic equations Linear differential equations Linear and non-linear differential equations

kvkumar answered in Numerical Methods Jun 29, 2016

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3 votes

2 answers

24

ISRO2009-51
The formula $P_k = y_0 + k \triangledown y_0+ \frac{k(k+1)}{2} \triangledown ^2 y_0 + \dots + \frac{k \dots (k+n-1)}{n!} \triangledown ^n y_0$ is Newton's backward formula Gauss forward formula Gauss backward formula Stirling's formula

naga praveen answered in Numerical Methods Jun 25, 2016

by naga praveen

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4 votes

2 answers

25

ISRO2011-52
Given X: 0 10 16 Y: 6 16 28 The interpolated value X=4 using piecewise linear interpolation is 11 4 22 10

Kapil answered in Numerical Methods Jun 24, 2016

by Kapil

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3 votes

1 answer

26

ISRO2009-47
The formula $\int\limits_{x0}^{xa} y(n) dx \simeq h/2 (y_0 + 2y_1 + \dots +2y_{n-1} + y_n) - h/12 (\triangledown y_n - \triangle y_0)$ $- h/24 (\triangledown ^2 y_n + \triangle ^2 y_0) -19h/720 (\triangledown ^3 y_n - \triangle ^3 y_0) \dots $ is called Simpson rule Trapezoidal rule Romberg's rule Gregory's formula

ManojK answered in Numerical Methods Jun 15, 2016

by ManojK

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4 votes

1 answer

27

ISRO2009-46
The shift operator $E$ is defined as $E [f(x_i)] = f (x_i+h)$ and $E'[f(x_i)]=f (x_i -h)$ then $\triangle$ (forward difference) in terms of $E$ is $E-1$ $E$ $1-E^{-1}$ $1-E$

Kapil answered in Numerical Methods Jun 15, 2016

by Kapil

7.9k views

5 votes

2 answers

28

GATE CSE 2000 | Question: 2.1
X, Y and Z are closed intervals of unit length on the real line. The overlap of X and Y is half a unit. The overlap of Y and Z is also half a unit. Let the overlap of X and Z be k units. Which of the following is true? k must be 1 k must be 0 k can take any value between 0 and 1 None of the above

confused_luck answered in Numerical Methods Jan 14, 2016

by confused_luck

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30 votes

3 answers

29

GATE CSE 2006 | Question: 1, ISRO2009-57
Consider the polynomial $p(x) = a_0 + a_1x + a_2x^2 + a_3x^3$ , where $a_i \neq 0$, $\forall i$. The minimum number of multiplications needed to evaluate $p$ on an input $x$ is: 3 4 6 9

srestha answered in Numerical Methods Nov 24, 2015

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6 votes

2 answers

30

GATE CSE 1999 | Question: 1.23
The Newton-Raphson method is to be used to find the root of the equation $f(x)=0$ where $x_o$ is the initial approximation and $f’$ is the derivative of $f$. The method converges always only if $f$ is a polynomial only if $f(x_o) <0$ none of the above

Rajarshi Sarkar answered in Numerical Methods Jun 24, 2015

by Rajarshi Sarkar

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1 answer

31

GATE CSE 1997 | Question: 4.10
The trapezoidal method to numerically obtain $\int_a^b f(x) dx$ has an error E bounded by $\frac{b-a}{12} h^2 \max f’’(x), x \in [a, b]$ where $h$ is the width of the trapezoids. The minimum number of trapezoids guaranteed to ensure $E \leq 10^{-4}$ in computing $\ln 7$ using $f=\frac{1}{x}$ is 60 100 600 10000

Digvijay Pandey answered in Numerical Methods Jun 6, 2015

by Digvijay Pandey

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2 votes

2 answers

32

GATE CSE 1997 | Question: 1.2
The Newton-Raphson method is used to find the root of the equation $X^2-2=0$. If the iterations are started from -1, the iterations will converge to -1 converge to $\sqrt{2}$ converge to $\sqrt{-2}$ not converge

Rajarshi Sarkar answered in Numerical Methods Jun 5, 2015

by Rajarshi Sarkar

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4 votes

2 answers

33

GATE CSE 1996 | Question: 2.5
Newton-Raphson iteration formula for finding $\sqrt[3]{c}$, where $c > 0$ is $x_{n+1}=\frac{2x_n^3 + \sqrt[3]{c}}{3x_n^2}$ $x_{n+1}=\frac{2x_n^3 - \sqrt[3]{c}}{3x_n^2}$ $x_{n+1}=\frac{2x_n^3 + c}{3x_n^2}$ $x_{n+1}=\frac{2x_n^3 - c}{3x_n^2}$

Rajarshi Sarkar answered in Numerical Methods Jun 4, 2015

by Rajarshi Sarkar

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3 answers

34

GATE CSE 1995 | Question: 2.15
The iteration formula to find the square root of a positive real number $b$ using the Newton Raphson method is $x_{k+1} = 3(x_k+b)/2x_k$ $x_{k+1} = (x_{k}^2+b)/2x_k$ $x_{k+1} = x_k-2x_k/\left(x^2_k+b\right)$ None of the above

Rajarshi Sarkar answered in Numerical Methods Jun 2, 2015

by Rajarshi Sarkar

2.2k views

1 vote

1 answer

35

GATE CSE 1993 | Question: 01.3
Simpson's rule for integration gives exact result when $f(x)$ is a polynomial of degree $1$ $2$ $3$ $4$

Rajarshi Sarkar answered in Numerical Methods Apr 26, 2015

by Rajarshi Sarkar

4.6k views

4 votes

1 answer

36

GATE IT 2007 | Question: 77
Consider the sequence $\left \langle x_n \right \rangle,\; n \geq 0$ defined by the recurrence relation $x_{n + 1} = c \cdot (x_n)^2 - 2$, where $c > 0$. For which of the following values of $c$, does there exist a non-empty open interval $(a, b)$ such that the ... $0.25$ $0.35$ $0.45$ $0.5$ i only i and ii only i, ii and iii only i, ii, iii and iv

Rajarshi Sarkar answered in Numerical Methods Apr 13, 2015

by Rajarshi Sarkar

1.2k views

3 votes

1 answer

37

GATE IT 2004 | Question: 38
If f(l) = 2, f(2) = 4 and f(4) = 16, what is the value of f(3) using Lagrange's interpolation formula? 8 8(1/3) 8(2/3) 9

Rajarshi Sarkar answered in Numerical Methods Apr 7, 2015

by Rajarshi Sarkar

2.9k views

12 votes

3 answers

38

GATE CSE 2015 Set 3 | Question: 50
The velocity $v$ (in kilometer/minute) of a motorbike which starts form rest, is given at fixed intervals of time $t$ (in minutes) as follows: t 2 4 6 8 10 12 14 16 18 20 v 10 18 25 29 32 20 11 5 2 0 The approximate distance (in kilometers) rounded to two places of decimals covered in 20 minutes using Simpson's $1/3^{rd}$ rule is ________.

ashishacm answered in Numerical Methods Feb 20, 2015

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8 votes

2 answers

39

GATE CSE 2015 Set 2 | Question: 39
The secant method is used to find the root of an equation $f(x)=0$. It is started from two distinct estimates $x_a$ and $x_b$ for the root. It is an iterative procedure involving linear interpolation to a root. The iteration stops if $f(x_b)$ is very small and then $x_b$ is ... $x_b - (x_b-x_a) f_b / (f_b-f(x_a)) $ $x_a - (x_b-x_a) f_a / (f_b-f(x_a)) $

Arjun answered in Numerical Methods Feb 20, 2015

by Arjun

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1 answer

40

calculus
The estimate of $\int_{0.5}^{1.5}\frac{dx}{x}$ obtained using Simpson’s rule with threepoint function evaluation exceeds the exact value by (A) 0.235 (B) 0.068 (C) 0.024 (D) 0.012

Nisha kumari asked in Numerical Methods Jan 30, 2015

by Nisha kumari

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